In this paper, a simple relation between the Leimkuhler curve and the mean residual life is established. The result is illustrated with several models commonly used in informetrics, such as exponential, Pareto and lognormal. Finally, relationships with some other reliability concepts are also...

Life expectancy, i.e., mean residual life function, has been of important practical and scientific interests to characterise the distribution of residual life. Regression models are often needed to model the association between life expectancy and its covariates. In this article, we consider a...

A wide selection of classical and recent tests for exponentiality are discussed and compared. The classical procedures include the statistics of Kolmogorov-Smirnov and Cramér-von Mises, a statistic based on spacings, and a method involving the score function. Among the most recent approaches...

In this paper we study a family of stochastic orders of random variables defined via the comparison of their percentile residual life functions. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are...

In this paper we study Arnold's (1987, Statist. Probab. Lett.5, 263-266) class of bivariate distributions with Pareto conditionals from a reliability point of view. Failure rates and mean residual life function of the marginal distributions and their monotonic properties are studied. The hazard...

We provide procedures to generate random variables with Lindley distribution, and also with Poisson–Lindley or zero-truncated Poisson–Lindley distribution, as simple alternatives to the existing algorithms. Our procedures are based on the fact that the quantile functions of these probability...

This study deals with the classical and Bayesian estimation of the parameters of a k-components load-sharing parallel system model in which each component's lifetime follows Lindley distribution. Initially, the failure rate of each of the k components in the system is h(t,θ1) until the first...

A treatment of the mathematical properties is provided for the Lindley distribution. The properties studied include: moments, cumulants, characteristic function, failure rate function, mean residual life function, mean deviations, Lorenz curve, stochastic ordering, entropies, asymptotic...